The Carmichael function, denoted as \(\lambda(n)\), is a function that gives the smallest positive integer \(m\) such that \(a^m \equiv 1 \mod n\) for every integer \(a\) that is coprime to \(n\). It generalizes the concept of the order of an element in modular arithmetic and is closely related to Euler's totient function, which counts the number of integers up to \(n\) that are coprime to it.
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